矩形网格扁壳结构的非线性振动

聂国华

矩形网格扁壳结构的非线性振动

聂国华

同济大学工程力学系上海

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出版历程
- 收稿日期: 1992-09-26
- 刊出日期: 1994-06-15

Non-Linear Vibration of Rectangular Retlculated Shallow Shell Structures

Nie Guo-hua

Department of Engineering Mechanics, Tongji Universitg, Shanghai

摘要

摘要: 本文运用作者已建立的矩形网格扁壳的非线性弹性理论,求解了该类结构的非线性振动问题。通过采用横向挠度（网格节点横向位移）和力函数的某种（广义）Fourier级数形式的设定解,由试函数的加权得到解中系数之间的关系和决定时间未知函数的振动方程,然后利用正则摄动法和迦辽金法推导出结构自由振动和谐和激励作用下结构非线性受迫振动的幅频关系,并给出了计算实例。
- 矩形网格扁壳 /
- 非线性 /
- 振动 /
- 幅频特征关系 /
- 梁振动特征函数
Abstract: This paper deals with non-linear vibration of rectangular reticulated shallow shells by applying non-linear elastic theory of such structures established by the author. Using the assumed(generalized) Fourier series solutions for transverse deflection(lattice joint transverse displacement) and force function，weighted means of the trial functions lead to the relations among the coefficients related to the solutions and vibration equation which determines the unknown time function, and then the amplitude-frequency relations for free vibration and forced vibration due to harmonic force are derived with the aid of the regular perturbation method and Galerkin procedure, respectively.Numerical ezamples are given as well.
- rectangular reticulated shallow shells /
- non-linear /
- vibration /
- characteristic amplitude-frequency relation /
- beam vibration eigenfunctions

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参考文献(16)

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